DNA damage is a major cause of replication interruption, mutations, and cell death. DNA damage is removed by several types of repair processes. The involvement of specialized DNA polymerases in replication provides an important mechanism that helps tolerate persistent DNA damage. Specialized DNA polymerases incorporate nucleotides opposite lesions with high efficiency but demonstrate low accuracy of DNA synthesis. In this review, we summarize the types and mechanisms of formation and repair of non-bulky DNA lesions, and we provide an overview of the role of specialized DNA polymerases in translesion DNA synthesis.